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The Language of Mathematics:

Towards an Equitable Mathematics Pedagogy

Nathaniel Rounds, PhD; Katie Horneland, PhD; Nari Carter, PhD

"Education, then, beyond all other devices of human origin, is the great equalizer of the conditions of men, the balance wheel of the social machinery."

(Horace Mann, 1848)

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?2020 Imagine Learning, Inc.

Introduction

From the earliest days of public education in the United States, educators have believed in education's power as an equalizing force, an institution that would ensure equity of opportunity for the diverse population of students in American schools. Yet, for as long as we have been inspired by Mann's vision, our history of segregation and exclusion reminds us that we have fallen short in practice. In 2019, 41% of 4th graders and 34% of 8th graders demonstrated proficiency in mathematics on the National Assessment of Educational Progress (NAEP). Yet only 20% of Black 4th graders and 28% of Hispanic 4th graders were proficient in mathematics, compared with only 14% of Black 8th grades and 20% of Hispanic 8th graders. Given these persistent inequities, how can education become "the great equalizer" that Mann envisioned? What, in short, is an equitable mathematics pedagogy?

The Language of Mathematics: Towards an Equitable Mathematics Pedagogy

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Mathematical Competencies

To help think through this question, we will examine the language of mathematics and the role of language in math classrooms. This role, of course, has changed over time. Ravitch gives us this picture of math instruction in the 1890s:

Some teachers used music to teach the alphabet and the multiplication tables..., with students marching up and down the isles of the classroom singing... "Five times five is twenty-five and five times six is thirty..." (Ravitch, 2001)

Such strategies for the rote learning of facts and algorithms once seemed like all we needed to do to teach mathematics. Yet, as educators in the twentieth century began to stress new mathematical competencies --such as solving novel problems, collaborating with peers, and sense-making-- tension arose between the need for fluency with facts and algorithms versus focus on conceptual understanding. At the height of the Math Wars in the 1990s, one author defended teaching algorithms like this:

Could these authors [who advocate against teaching algorithms] be unaware of the fact that the addition algorithm, like all other standard algorithms, contains mathematical reasoning that would ultimately enhance children's understanding of our decimal number system? Why not consider the alternative approach of teaching these algorithms properly before advocating their banishment from classrooms? (Wu, 1999)

In the twenty-first century, next generation standards, including the Common Core State Standards for Mathematics (CCSSM) and the individual states' own mathematical frameworks, have tried to strike an appropriate balance between the need for fluency with skills and conceptual understanding. Yet, even as most educators now agree that such a balance must be found, it can be bewildering to try and integrate into classroom practice all the aspects of math instruction that researchers now recommend.

To help educators navigate the multiple skills, capacities and proficiencies demanded by the discipline, Moschkovich (2015) suggests we examine the multiple competencies required for what she terms academic literacy in mathematics. These are:

1. Cognitive competencies including procedural fluency, conceptual understanding, metacognitive behaviors such as a growth mindset, and productive beliefs about the utility of mathematics.

2. Cultural competencies necessary for participating in the cultural practice of mathematics, including "problem solving, sense-making, reasoning, modeling, and looking for patterns, structure, or regularity." (Moschkovich, 2015, p. 1068) These competencies are articulated by frameworks such as the CCSS Standards for Mathematical Practice.

3. Communicative competencies necessary for communicating with others about mathematics, both in spoken word, writing, and symbols, and in both the everyday register and the academic register.

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?2020 Imagine Learning, Inc.

Moschkovich (2015) names these competencies mathematical proficiency, mathematical practice, and mathematical discourse. Though Moschkovich focused on academic literacy in mathematics for English learners, we believe her framework is illuminating for all educators and all students.

In this paper, we use Moschkovich's schema as a starting point to explore the necessary role of language in mathematics classrooms. We examine, in turn, mathematical proficiency, practice, and discourse, and implications of each for classroom practice. We also consider the lens of special student populations. We hope through these investigations to articulate the necessary components of equitable mathematics pedagogy.

The Language of Mathematics: Towards an Equitable Mathematics Pedagogy

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